One of our S Corp (Multi member LLC) members resigned and was paid a buyout. There are still other members. How do I report that buyout? Is that on a 1099?

Several items need to be addressed here:

1. To answer your specific question, the buyout distribution is reported on a 1099-DIV as a liquidating distribution in box 9.
2. In addition to providing the former member with the 1099, you will need to file a copy of this with the IRS using form 1096.
3. Additionally, you need to decide on the allocation of the income / loss.  You have two options:
1. Normal per day per share
2. Closing of the books.  To use this you will need to make an election.  This effectively treats the earnings as if they were earned in two separate periods.  This can be a significant issue depending on the earnings or loss of the S corporation.
4. The K-1 needs to be marked final.  Make sure that the only distributions reflected on the K-1 are normal distributions and not the final liquidating distribution.
5. Depending on the $$ involved, you may want to consult with a tax professional.

Where is that 1099-DIV  buyout recorded in turbo tax?

The shareholder will record this sale just as any other sale of security / stock on their 1040.
This will be the sales price on Sch D and the applicable form 8949.  Their basis in the stock will be the cost basis.